Most of the economic literature on bargaining has focused on situations where the set of possible outcomes is taken as given. This paper is concerned with situations where decision-makers first need to identify the set of feasible outcomes before they bargain over which of them is selected. Our objective is to understand how different bargaining institutions affect the incentives to disclose possible solutions to the bargaining problem, where inefficiency may arise when both parties withold Pareto superior options. We take a first step in this direction by proposing a simple, stylized model that captures the idea that bargainers may strategically withhold information regarding the existence of feasible alternatives that are Pareto superior. We characterize a partial ordering of regular bargaining solutions (i.e., those belonging to some class of natural solutions) according to the likelihood of disclosure that they induce. This ordering identities the best solution in this class, which favors the weaker bargainer subject to the regularity constraints. We also illustrate our result in a simple environment where the best solution coincides with Nash, and where the Kalai-Smorodinsky solution is ranked above Raiffa's simple coin-toss solution. The analysis is extended to a dynamic setting in which the bargainers can choose the timing of disclosure.